Optical micro-profilometry for archaeology

Pierluigi Carcagnì

a, Claudia Daffara

b, Raffaella Fontana*

b, Maria Chiara Gambino

b,

Maria Mastroiannib, Cinazia Mazzotta

c, Enrico Pampaloni

b, Luca Pezzati

b

aIstituto Nazionale di Ottica Applicata – Sez. di Lecce, via Barsanti, 73010 Arnesano (LE), Italy

bIstituto Nazionale di Ottica Applicata - Largo E. Fermi 6 – 50125 Firenze, Italy

cDipartimento di Beni Culturali, Università di Lecce, via D. Birago 64, 73100 Lecce, Italy

ABSTRACT

A quantitative morphological analysis of archaeological objects represents an important element for historical

evaluations, artistic studies and conservation projects.

At present, a variety of contact instruments for high-resolution surface survey is available on the market, but because of

their invasivity they are not well received in the field of artwork conservation. On the contrary, optical testing techniques

have seen a successful growth in last few years due to their effectiveness and safety.

In this work we present a few examples of application of high-resolution 3D techniques for the survey of archaeological

objects.

Measurements were carried out by means of an optical micro-profilometer composed of a commercial conoprobe

mounted on a scanning device that allows a maximum sampled area of 280×280 mm2.

Measurements as well as roughness calculations were carried out on selected areas, representative of the differently

degraded surface, of an ellenestic bronze statue to document the surface corrosion before restoration intervention started.

Two highly-corroded ancient coins and a limestone column were surveyed to enhance the relief of inscriptions and

drawings for dating purposes.

High-resolution 3D survey, beyond the faithful representation of objects, makes it possible to display the surface in an

image format that can be processed by means of image processing software. The application of digital filters as well as

rendering techniques easies the readability of the smallest details.

Keywords: roughness, 3D survey, digital model, micro-profilometer, scanning device, conoprobe, archeometry.

1. INTRODUCTION

Optical techniques are widely diffused and extremely well received in the field of conservation because of their

effectiveness and safety [1-5]. The characteristics of being non-invasive make them particularly suitable for measuring

frail (and precious!) objects. Many optical devices for three-dimensional survey are derived from industrial metrology,

but the peculiarity of each artwork does not allow for a straightforward application. Challenges in artwork diagnostics

are mainly due to shape irregularity and polychromy as well as the high-accuracy required to catch even the smallest

details of a work of art.

Surface cleaning is one of the most important and sometimes controversial stages of the conservation process: decisions

have to be made regarding partial or complete removal of the outer patina, and restorers and conservators work would be

considerably helped by the knowledge of surface morphology. A process of surface examination and analysis is, thus,

critical to the definition and interpretation of corrosion or degradation in order to plan the restoration intervention.

Moreover, a statistical analysis based on roughness calculation, can assess the condition of the object surface to monitor

changes due to restoration intervention, surface decay due to wearing agents, or the evolution with time in terms of shape

variations. When describing the surface integrity of an artwork, in fact, an important parameter to deal with it is

roughness [6].

*lella@ino.it; phone: + 39 055 23.08.313; fax: +39 055 233.77.55; www.ino.it; http://arte.ino.it

Every surface has a certain amount of microscopic roughness, even if only at a molecular level, and the defects or

features which contribute to it may be either random or regular (periodic). For instance, roughness measurements are the

basis of many industrial quality controls: in this case, the roughness arises from the working process.

Generally speaking, the surface of an object can be described by three parameters, according to the spatial frequencies

considered: form (low frequencies), waviness (mid frequencies) and roughness (high frequencies or short wavelengths).

The three frequency ranges depend on the object dimensions and manufacturing: for instance, for an optical component,

shape is related to the designed form, waviness is related to the deviation between projected and manufactured form, and

roughness is the surface irregularity that causes light scattering. The UNI ISO 468 [7] norm reports on a relation between

an object manufacturing method and the roughness parameters. However there are no case studies that conclusively

prove this relationship, and, furthermore, artworks cannot be classified in any of the standard engineering surface

categories, neither for materials, nor for manufacture.

Roughness computation deriving from a shape survey is quite a new application in the Cultural Heritage field [8]. The

main problem when dealing with artworks is the lack of rules defining both a measurement and an analysis protocol for

cultural heritage applications.

In this work we present the preliminary results concerning statistical analysis carried out on one area, representative of

the corroded surface, of an Hellenistic bronze statue. Determination of the roughness and its relative characteristic

wavelength was carried out before the cleaning process started, and measurements will be repeated after the restoration

intervention.

Image processing was applied to a few images of archaeological findings in order to make out inscriptions and to

enhance their readability. Snapshots were obtained from the high-resolution digital model of the surface.

All the three-dimensional surveys were carried out by means of a high-resolution laser scanning micro-profilometer.

2. THREE-DIMENSIONAL SURVEY OF ARCHAEOLOGICAL FINDINGS

The archaeological survey differs from any other kind of survey mainly because of two reasons: the first one is the huge

variety of the objects of interest, ranging from buildings to skeletons, from wreckages to statues, etc. The second one is

the lack of generally accepted measurement standards. For example, the archaeological drawing, which is presented as a

scientific document that is supposed to reproduce the reality through the graphic interpretation following given criteria

and rules, remains, to a certain extent, a subjective interpretation of reality. Therefore the application of a method clearly

expressed in its rules is foreboded.

In each single case, researchers have the opportunity/freedom to choose the best suited technique, the graphic code for

representation and the set of objects that is representative of the whole site to be documented.

For this purpose, both a deep knowledge of the above mentioned objects and the possibility of measuring different

objects in different contexts is necessary.

The final goal of an extensive archaeological survey is the acquisition of meaningful and intrinsically correct data so to

compare the results from different techniques for the documentation and historical interpretation of an archaeological

finding.

Up to now, archaeological findings were recorded by means of photographs, relying, thus, on the photographer and

drawer skill. This kind of information is only qualitative, lacking of any quota information that is usually obtained by

means of contact techniques (stylus profilometer) or, otherwise, by means of optical instruments based on light scattering

that, by integrating over a macroscopic area (in the cm2

range) are not well suited for a proper detailed reproduction. Alternatively, a variety of microscopes is available, but only for laboratory applications and all of them entail micro-

sampling.

In this work we present an application of the optical micro-profilometry to some archaeological findings. Besides a high-

resolution three-dimensional documentation, not achievable with any photographic image, this technique allows a data

post-processing that can lead to either an increase in inscription readability (imaging analysis) or roughness computation

(statistical analysis).

2.1. The optical micro-profilometer

The optical micro-profilometer realized at INOA (National Institute for Applied Optics, Florence) is composed of a

commercial conoscopic probe mounted on two motorized high-precision linear stages. The probe (Conoprobe 1000 by

Optimet) working principle is as follows: a light beam projected by a diode laser on the sample is both reflected and back

scattered, and it impinges on a uniaxial birefringent crystal placed between two circular polarizers (see Fig. 1). The

ordinary and the extraordinary beams are then generated inside the crystal and produce an interference pattern [9, 10].

Surface height is computed from intensity and phase information on the interference pattern: quota differences result in

optical path differences that are seen as light and dark fringes on the CCD camera. The probe we used is equipped with a

50 mm lens which sets a quota resolution of nearly 1 µm and a dynamic range of 8 mm at a stand-off distance about 40

mm. The overall accuracy is better than 6 µm.

Surface shape is obtainable by mechanical, non-contact scanning. The scanning device is composed of two motorized

high-precision (0.1 µm) linear stages, that are perpendicularly assembled. The system allows measurement on a

maximum area of about 300×300 mm2. The instrument has a maximum transversal resolution of 20 µm, with an

acquisition speed ranging from 100 to 400 point/s depending on the set spatial sampling frequency. The whole system is

computer controlled.

The micro-profilometer allows measurements on surfaces with almost any reflectivity, with an incident angle up to 85°,

that is to say, scanning at very close to grazing incidence is possible. Therefore, the survey of very small details, like

holes of < 1 mm diameter and 25:1 ratio between quota and diameter, is possible [11]. Besides, the instrument is not

sensitive to color gradients being, therefore, also suitable for the survey of surfaces characterized by high chromatic

contrast [12]. These characteristics, combined with co-linearity, allow the measuring of thin grooves and deep holes.

Figure 1: Conoscopic probe working principle.

3. APPLICATIONS

3.1. The Minerva of Arezzo

The Minerva of Arezzo is a bronze statue discovered in Arezzo in 1541 (see Fig. 2) whose origin is still uncertain: it

could be either an original Hellenistic bronze dating back to third century B.C., or a variant produced in the Roman

Imperial period (first century A.C.). The statue, usually located at the Archaeological Museum in Florence, is currently

under repair at the Archaeological Restoration Centre of the Tuscany Region in Florence. Restoration was considered

very urgent because of the highly endangered status of the statue (precarious conditions of the structural wooden

elements inside the statue and extensive corrosion of the bronze layer). Besides that, the statue was extensively restored

in the past (the main restorations date back to the sixteenth and eighteenth centuries), and these actions modified in a

significant manner the aspect and integrity of the artwork. As an example, a missing arm (the right one) was replaced in

eighteenth century restoration; plaster was used to join disconnected bronze sections and to fill gaps; finally a dark

greenish paint covers most of the statue surface, giving a uniform aspect to plaster and bronze sections, but actually

covering the original patina.

The statue was completely demounted in its parts, and, in order to keep trace of the surface corrosion before restoration

started, a three-dimensional survey was carried out on a few differently corroded areas, representative of the differently

degraded statue surface (pony-tail, helmet, shoulder, dress, armour). “Bronze disease” is one of the most serious hazards

of bronze. This disease takes the form of a sudden outbreak of small patches of corrosion and is distinguished by rough,

light green spots.

Each investigated area is 4×5 cm2 and was sampled with a 50 µm step, corresponding to a range map of 801×1001

points.

Figure 2: The Minerva of Arezzo.

Analysis of surface features was carried out by using the three-dimensional data set. Actual surface data is made of a set

of 2D heights data acquired in parallel trace lengths to form the final 3D data set. In order to compute the roughness, a

suitable evaluation surface was taken consisting in a selected region of interest (ROI) of 201×201 sampled points, i.e. a 1

cm squared sized area. In other words, the ROI is representative of the surface pattern superimposed to a form as regular

as possible, e.g. plane or conic.

The first step was removing the mean form by least squares fit. The regression 2nd order polynomial (Zform) was

subtracted from the 3D surface data (Z) to give the conditioned surface Zcond = Z - Zform (see Fig. 3a and 3b).

This resulting conditioned surface represents a surface texture including both the spatial features at short wavelength

(roughness) and the components at longer wavelength (waviness). Roughness is related to the microstructure of the

surface material whereas waviness is the surface deviation from the projected form. The spatial length at which

roughness becomes waviness is not a set point for Cultural Heritage applications, especially in case of archaeological

surfaces whose conservation state depends on many different factors. For this reason we investigated the roughness

texture at different spatial lengths.

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Figure 3a: ROI on the Minerva shoulder Figure 3b: Corresponding conditioned ROI

As a first step, a number of surface parameters were calculated for the unfiltered 3D data, i.e. data including waviness

and roughness, and the results are reported in table 1. Amplitude statistical parameters include the root-mean-square

deviation of the surface Sq (i.e. the RMS roughness), the average roughness Sa, the skewness Ss and the kurtosis Sk of

topography heights distribution. The maximum peak-valley z height St is also reported. The hybrid parameters ∆q and ∆a

(i.e. the RMS slope and average slope of the surface within the sampling ROI) have been calculated, as well as the RMS

wavelength λq and the average wavelength λa of the surface.

Sq Sa St Ss Sk ∆q ∆a λq λa

33.0812 26.3542 315.5556 0.0586 3.2868 0.1939 0.1516 1.0718e+003 1.0924e+003

Table 1: Parameters of the unfiltered 3D surface (roughness + waviness), in micron.

The second step was to isolate the roughness information from the matrix data by use of filtering. A Gaussian filter,

which is phase correct, was used to separate the surface into long-wave components, forming the wavy surface, and

short-wave components, belonging to the roughness. A roughness filter with a cut-off value of λc removes the

wavelengths above λ c on the surface by reducing their amplitude, allowing to assess the wavelengths below λ c which

form the roughness. The choice of the cut-off depends on the nature of the surface texture, i.e. on the expected roughness

values. Increasing the cut-off means that longer spatial wavelength, i.e. wider features, are included into the roughness

computation.

A number of different cut-off lengths were used to calculate the surface parameters both for waviness and for roughness,

and the results are reported in table 2. Figures 4a, 4b, 4c, 4d show the surface roughness and waviness at different spatial

lengths and figure 5 shows the 2D profiles.

Cut-off 250 micron

Roughness Waviness

Sq 6.2526 Sq 31.1425

Sa 4.5768 Sa 25.0431

St 112.1911 St 267.7769

Ss 0.2943 Ss -0.0672

Sk 6.7457 Sk 3.0058

∆q 0.1188 ∆q 0.1126

∆a 0.0966 ∆a 0.0855

λq 330.6741 λq 1.7380e+003

λa 297.7700 λa 1.8411e+003

Cut-off 500 micron

Roughness Waviness

Sq 8.7262 Sq 29.8253

Sa 6.1555 Sa 24.1334

St 157.5151 St 210.7117

Ss 1.0044 Ss -0.1347

Sk 10.4131 Sk 2.7729

∆q 0.1610 ∆q 0.0754

∆a 0.1272 ∆a 0.0605

λq 340.5697 λq 2.4854e+003

λa 304.1107 λa 2.5074e+003

Cut-off 1 mm

Roughness Waviness

Sq 11.2618 Sq 27.8183

Sa 7.6770 Sa 22.8903

St 203.5827 St 166.9511

Ss 1.9010 Ss -0.2356

Sk 17.5978 Sk 2.4425

∆q 0.1814 ∆q 0.0512

∆a 0.1397 ∆a 0.0436

λq 390.1792 λq 3.4130e+003

λa 345.2002 λa 3.2959e+003

Cut-off 2 mm

Roughness Waviness

Sq 14.4861 Sq 24.6830

Sa 10.2829 Sa 20.6494

St 238.0447 St 108.3560

Ss 1.3994 Ss -0.4338

Sk 13.6008 Sk 2.2358

∆q 0.1885 ∆q 0.0346

∆a 0.1445 ∆a 0.0305

λq 482.7819 λq 4.4865e+003

λa 447.1971 λa 4.2496e+003

Table 2: Surface parameters for roughness and waviness at different cut-off lengths, in micron.

Figure 4a: Surface roughness and waviness with the 250 µm cutoff .

Figure 4b: Surface roughness and waviness with the 500 µm cutoff .

Figure 4c: Surface roughness and waviness with the 1 mm cutoff .

Figure 4d: Surface roughness and waviness with the 2 mm cutoff .

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Figure 5: 2D profiles over 100 points for each wavelength cut-off.

3.2. Ancient coins

Two bronze coins, kept at the Cultural Heritage Department of the University of Lecce, were measured.

The first one (see Fig. 6a, 6b), coined from Capua mint, is a Greek coin probably dated the beginning of III century B.C.

The second one is a Roman coin (see Fig. 3c, 3d) probably dated the end of III sec. B.C.

Range maps of 40×50 mm2 with 50 µm sampling step were acquired, corresponding to range maps of 801×1001 points.

Figure 6a: Greek coin photograph, obverse side.

Figure 6b: Greek coin photograph, reverse side.

Figure 6c: Roman coin photograph, obverse side.

Figure 6d: Roman coin photograph, reverse side.

Snapshots from the 3D data acquisitions were taken and processed, to emphasize the inscriptions on the coin surfaces

and increase their readability.

In figure 7 a few example of image processing are shown, where embossing filtering and raking light simulation

were used. On the obverse side of the Greek coin (see Fig. 7a) a human head belonging to Apollo is clearly visible,

according to the archaeologists opinion; on its reverse side a lyre and the inscription kapu [13] is represented (see

Fig. 7b). Due to the highly corrupted surface of the Roman coin, result interpretation was difficult. On the obverse

side, the two-faced Janus head can be hardly seen (see Fig. 7c), whereas on the reverse side a prow of a ship is

probably present (see Fig. 7d). The two images of the drawing of the coin type are also shown (see Fig. 7e, 7f).

Figure 7a: Greek coin, obverse side.

Figure 7b: Greek coin, reverse side.

Figure 7c: Roman coin, obverse side.

Figure 7d: Roman coin, reverse side.

Figure 7e: Drawing of the Greek coin type. Figure 7f: Drawing of the Roman coin type.

For the numismatist the primary source of knowledge of a coin history is contained in the inscriptions. The

quantitative morphological characterization of coin surface and the subsequent possibility of image processing is,

thus, a new approach that could completely change the way to document archaeological findings.

3.3. Column

A gypsum mould of a small column was surveyed. The column is 37 cm high and has a diameter of about 20 cm. It was

discovered, by chance, by a private person in Patù (Lecce) and only recently it has been acquired by the Museum

Sigismondo Castromediano in Lecce.

On the column surface messapic inscriptions, dated back the end of VI sec. B.C., as well as drawing representing boats,

are present.

The necessity of a quantitative survey derived from the many consumptions present on the surface, that compromised a

good rendering of micro-relieves by means of photography.

In figure 8a the software acquisition interface is shown. From the profile width and depth, in both the x, y transversal

directions, the shape of the grooves can be reconstructed in order to investigate the kind of tools used for the inscriptions.

In figure 8b the grooves shape is enhanced in two different orientations of the digital model.

Figure 8a: Grey-scale map as appearing in the software acquisition interface.

Figure 8b: Snapshots taken from the digital model, for different orientations of the simulated raking light.

4. CONCLUSIONS

In this work an application to archaeological findings of three-dimensional survey by means of conoscopic micro-

profilometry was presented. The instrument high quota resolution allows the realization of an accurate digital model that

faithfully reproduces the original object. A few examples of 3D archaeological surveys were reported: roughness

measurements on the Minerva of Arezzo, an Hellenistic bronze statue, to document the corroded surface before

restoration started; surface reproduction of two ancient coins, to enhance the readability of the inscriptions and ease a

correct dating; morphologic studies on an ancient column, to trace back to the tools used for the inscriptions.

The quantitative representation of the surface of an object has many relapses in the archaeological field, ranging from the

analysis of the artwork condition to the support for restoration intervention, from the realization of 3D catalogues and

archives to the monitoring of the various phases of the repair plan. Moreover, it is possible to realize no-contact moulds

starting from the three-dimensional surface survey.

A quantitative analysis of archaeological findings is foreboded to overcome the lack of generally accepted measurement

standards. The three-dimensional survey is intrinsically free from the subjective interpretation of reality, characteristic of

the archaeological drawing.

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